Of course it is possible! Around 25% of the world's steel is already produced by electric arc furnaces. 100% in some countries, and over 70% in the USA.

The UK exports 7-8 million tonnes of scrap steel every year, while producing about 5 million tonnes in blast furnaces. There's more than enough feedstock to replace all the UK blast furnace steel production with EAFs and still have some left over.